Sage advice from Kelley Grayson who has a long standing and popular blog at Ambulance Driver Files. He's is also a much sought after speaker for EMT / First Responder type industry conference. Much influence, he has.

On the prospect of someone filming in public, he offers some good advice to his fellow professionals which starts out with ....

If you are ever in public, performing your duties as an EMT, or cop, or firefighter, and you realize someone is filming you, hereís what you do:

Listen carefully, now. This is important. The instructions Iím going to give you must be followed to the letter. Do not deviate from them, and I guarantee you will handle the situation as best as can reasonably be expected: Do. Your. Job.